Question

Find the sum of all natural numbers between $250$ and $1000$ which are exactly divisible by $3$.

Answer 1

Clearly the numbers between $250$ and $1000$ which are divisible by $3$ are $252$, $255$, $258$,________ $999$.
$\therefore T_n=999=a+(n-1)d=252+(n-1)3$
$333=84+n-1$
$\therefore n=333-83=250$
$\therefore S=\frac{n}{2}[a+l]=\left(250/2\right)[252+999]$
$=125\times 1251=156375$.